Homework #4 An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU. 1) What is the semi major axis of its orbit? 2) What is the period of its orbit? 3) What is it’s eccentricity?

Homework #4 continued 4) A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later? 5) How tall is the Empire State Building? 6) An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

Homework #4 last page 7) What is the maximum resolution of your eyes (assume the wavelength range that your eyes are sensitive to is 300 – 700 nm and that your iris is ½ cm in diameter. 8) What size eye would be required to see in the radio with the same maximum resolution of your eyes? (use 21 cm for the wavelength of typical radio waves) 9) What is the maximum resolution of the VLBA (longest baseline = 5000 km) at a wavelength of 21 cm?

Angular Resolution: D

You can also go over wavelength, frequency, and speed with this tool from the Light and Spectroscopy tutorial.

Light as a Wave For a wave, its speed is: v =  f [distance/time] But the speed of light is a constant c = 3 x 108 m/s For light:  f = c and f = c /  The higher f is, the smaller  is, and vice versa. Our eyes recognize f (or ) as color!

Light as a Particle Light can also be treated as photons – packets of energy. The energy carried by each photon depends on its frequency (color) E = hf = hc /  (h = 6.6 x 10-34 J s) Bluer light carries more energy per photon.

Interaction of Light with Matter Remember that each electron is only allowed to have certain energies in an atom. Electrons can absorb light and gain energy or emit light when they lose energy. Hydrogen It is easiest to think of light as a photon when discussing its interaction with matter. Only photons whose energies (colors) match the “jump” in electron energy levels can be emitted or absorbed.

Light as Information Bearer We can separate light into its different wavelengths (spectrum). By studying the spectrum of an object, we can learn its: Composition Temperature Velocity

This tool from the Light and Spectroscopy tutorial.

Dividing Light Into a Spectrum Astronomers separate out light into its individual components using a diffraction grating or using a prism - then they analyze each part independently!

blue 460 nm 81 Filter Detector 81

blue 460 nm 81 green 530 nm 85 Filter Detector 85

blue 460 nm 81 green 530 nm 85 yellow 580 nm 83 Filter Detector 83

blue 460 nm 81 green 530 nm 85 yellow 580 nm 83 orange 610 nm 78 Filter Detector 78

blue 460 nm 81 green 530 nm 85 yellow 580 nm 83 orange 610 nm 78 Filter red 660 nm 70 Detector 70 The spectrum is continuous. UV IR

Natural Spectra ????

Änuenue (rainbow) Light from the Sun Water droplet

Shine Light through Hydrogen…

Shine Light through Hydrogen…

Shine Light through Hydrogen… 397 434 486 656 410

E = hn = hc/l g l = hc/E E = hn E = hn = hc/l l (mm) = (mm=10-6m) h=Planck’s constant; n=frequency [Hz=1/s]; l=wavelength [m] l (mm) = (mm=10-6m) E [eV] 1.24 [mm eV]

397 434 486 656 410 E(3 g 2) = 12.07-10.19 = 1.89 eV

l (mm) = (mm=10-6m) E [eV] 1.24 [mm eV] l(3 g 2) = ~ 0.656 mm 1.89 1.24

Shine Light through Hydrogen… 397 434 486 656 410

Thermal Radiation

Rules for Emission by Opaque Objects Hotter objects emit more total radiation per unit surface area. Stephan-Boltzmann Law: E = T4 (s = 5.7 x 10-8 [Watt/m2Kelvin4]) Hotter objects emit bluer photons (with a higher average energy.) Wien Law: max = 2.9 x 106 / T (K) [nm]

Two kinds of Spectra: 1) Absorption If light shines through a gas, each element will absorb those photons whose colors match their electron energy levels. The resulting absorption line spectrum has all colors minus those that were absorbed. We can determine which elements are present in an object by identifying emission & absorption lines.

2) Emission Spectra The atoms of each element have their own distinctive set of electron energy levels. Each element emits its own pattern of colors, like fingerprints. If it is a hot gas, we see only these colors, called an emission line spectrum.

Lets look at continuous, absorption line, and emission line spectra –

Kirchhoff’s Laws I. A hot, dense glowing object (solid or gas) emits a continuous spectrum.

Kirchhoff’s Laws II. A hot, low density gas emits light of only certain wavelengths -- an emission line spectrum.

Kirchhoff’s Laws III. When light having a continuous spectrum passes through a cool gas, dark lines appear in the continuous spectrum – an absorption line spectrum.

Kirchhoff’s Laws I III II

Telescopes

Astronomical objects emit all of these different kinds of radiation in varying amounts

Mm/Submm

Maunakea’s height